Question

What is the measurement for the exterior angle

Answer 1

First we find
`\angle ACB`

`\angle ACB = 180 - (4x - 100) = 180 - 4x + 100 = 280 - 4x`

Then we find a equation for all the interior angles

`180 = \angle ACB + \angle BAC + \angle ABC\\= 280 - 4x + x + 20 + x\\300 - 2x`

We solve for x

`180 = 300 - 2x\\180 - 300 = -2x\\-120 = -2x\\2x = 120\\x = 60\\`

Now we find the exterior angle

`\angle DCB = 4x - 100 = 4 \cdot 60 - 100 = 240 - 100 = 140`